Measure-valued analysis of stochastic populations

该项目旨在开发新的数学模型和工具，对受内部竞争和反馈影响的非常普遍的随机总体进行严格分析。拟议的数学框架是度量值过程的数学框架，这种设置需要包含这类系统固有的复杂性和随机结构。这类模型在进化生物学、细胞动力学和癌症研究中有着现实的应用，对于我们理解地方病的持久性和濒危物种的保护是必不可少的。这一项目的结果有望为复杂随机总体的行为和(不)稳定性提供洞察，并为其管理提供指导。

The project aims to develop new mathematical models and tools for the rigorous analysis of very general stochastic populations that are subject to internal competition and feedback. The proposed mathematical framework is that of measure-valued processes, a setting needed to encompass the complexity and random structure inherent in such systems. Models of this kind have real-world applications in evolutionary biology, cell kinetics and cancer research, and are essential to our understanding of the persistence of endemic disease and of the preservation of endangered species. The results of this project are expected to provide insight into the behaviour and (in-)stabilities of complex stochastic populations, and offer guidance for their management.